No other service Uncle Sam provides gets as up-close and personal as mail delivery.

Mail carriers come to our doors almost every day. They sometimes see us in ways only allowed for loved ones’ eyes: unwashed, unbrushed and maybe even undressed. They bring the good — wedding invitations and birth announcements — and the bad — overdue bills, a parent’s death certificate.

So the financial distress of the U.S. Postal Service can have personal implications for everyone, particularly its employees, who are both USPS workers and customers. Last week, the Senate approved legislation that is designed to help rescue the Postal Service from its budgetary sinkhole.

How well the bill would do that is debateable.

Sen. Joseph I. Lieberman (I-Conn.), a sponsor of the bill, said it would “remove some of the immediate financial pressure on the Postal Service” and encourage long-term innovative thinking and measures to reduce excess capacity, while “avoiding extreme changes that could further destabilize USPS.”

But the legislation leaves postal union leaders ambivalent, at best.

John F. Hegarty, president of the National Postal Mail Handlers Union, said: “We’re not endorsing it whole­­heartedly. We’ve come out in cautious support, recognizing there are still some improvements that need to be made.”

James Sauber, chief of staff for the National Association of Letter Carriers, said: “We’re sort of disappointed. . . . It’s sort of a missed opportunity, sort of tinkering around the edges.”

And Greg Bell, executive vice president of the American Postal Workers Union, said: “It’s an improvement over the original bill, [but] we have some issues.”

The first issue Bell cited is a provision in the legislation that would reduce some workers’ compensation payments three years after enactment, not including those who are totally and permanently disabled or already above retirement age. This would apply to federal employees generally, not just postal workers.

That measure “cracks down on fraud, making the system fairer, and encouraging a return to work for employees who are able to work,” says a statement from the office of Sen. Susan Collins (R-Maine), author of the provision and a co-sponsor of the overall legislation.

But that provision was enough to earn the opposition of Sen. Daniel K. Akaka (D-Hawaii), chairman of the subcommittee on the federal workforce, although he supported many other sections.

“Unfortunately, I cannot support a bill that cuts benefits for federal employees who have been injured in service to their country,” he said. “It is simply cruel to change the rules after-the-fact for disabled employees who were relying on the promise of these benefits. I’m disappointed my amendment to fix this issue was defeated.”

Another provision that could affect all federal employees allows the Postal Service to set up its own employee health insurance plan and withdraw from the Federal Employees Health Benefits Program. But Sen. John D. Rockefeller IV (D-W.Va.) may have undermined the push by postal officials to do that with his amendment, which would require any new postal program to have the same quality as the current government-wide program.

The major drain on Postal Service finances has been the congressionally imposed requirement to prefund retiree health benefits. It’s a requirement no other federal agency must meet.

Last year, officials said the USPS would have made about $1 billion from 2007 to 2010, instead of losing money, if they did not have the prefunding requirement. At that point, relieving service of that burden essentially would have solved its problems. At least in theory.

“However, that is no longer the case due to the deepening decline of first-class mail volume, our most ‘profitable’ product,” said David Partenheimer, a USPS spokesman. “This decline is expected to continue.”

Prefunding still accounts for 84 percent of the agency’s net loses. “The Postal Service has had over $25 billion of cumulative net losses in the past five fiscal years, which included $21 billion of the prefunding,” Partenheimer said.

The legislation provides significant but not total relief on this front, including cancellation of the 2011 through 2017 payments. Prefunding also would be at the 80 percent level, over 40 years, instead of 100 percent over 10 years. None of this, by the way, affects the health benefits retirees actually receive.

A postal issue that has drawn some of the greatest attention is the proposal to move to five-day delivery. Surveys show support for cutting Saturday delivery. That would not be allowed immediately under the legislation, but it could happen after two years if certain conditions are met.

That would cost 80,000 jobs, according to the National Association of Letter Carriers. It would save $2.7 billion annually (down from last year’s estimate of $3.1 billion), according to the Postal Service, or 3.9 percent of the $69.5 billion USPS budget. The Postal Rate Commission, however, says the USPS overstates the savings and says a more modest $1.7 billion is closer to the truth.

Either way, union officials argue, a budget savings of less than 4 percent for a 17 percent cut in service — which is what dropping one day of six amounts to — is a lopsided bargain.